Borders between countries will become "irrelevant" by the end of the century and the UK should prepare for that, John McDonnell has said.
The shadow chancellor said a borderless world was inevitable and people were already "ignoring" existing borders.
He also said the UK should be doing more to help the millions of migrants arriving in the European Union.
Mr McDonnell gave a speech in 2013 in which he suggested borders could become a thing of the past.
Asked to elaborate on this theory, by writer Rahil Gupta, Mr McDonnell said: "Inevitably in this century we will have open borders. We are seeing it in Europe already.
"The movement of peoples across the globe will mean that borders are almost going to become irrelevant by the end of this century so we should be preparing for that and explaining why people move."
In an interview with the BBC's Sunday Politics, he said borders will become increasingly difficult to maintain over the next 75 years and will eventually disappear, adding: "We should be opening up the debate of how we handle that."
Mr McDonnell stressed the need to deal with the causes of mass migration: Poverty, conflict and climate change but added: "We are seeing people ignoring borders already as they fly from Syria."
Current estimates suggest close to four million migrants will arrive in the EU between 2015 and 2017.
Mr McDonnell said the UK should take its fair share of that number.
He was unable to say how many people the UK should help but suggested the country should be a part of the EU's refugee quota scheme.
"I think we should cooperate with others and carry the burden because we are seeing, as in the refugee crisis, the majority of Britons want us to rise to that and ensure that we assist others and that others aren't suffering and that we don't stand on one side while people suffer."